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Let us calculate #5.Extension of ¢(s) from {Re s > 1} to {Res > 0}

Figure 2 Let us calculate #5.Extension of ¢(s) from {Re s > 1} to {Res > 0}

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Holomorphic extension domain from the right half-plane to the left half-plane Before we give more information about the function C(s), we mention that each of the two previous equations, give an extension of C(s) on the entire plane C except s = 1, as itis illustrated in Fig. 4. The gamma function was alreadv known to Euler. It generalizes the factonal n!. namelv The gamma function was already known to Euler. It generalizes the factorial n!, namely
Holomorphic extension domain from the right half-plane to the left half-plane Before we give more information about the function C(s), we mention that each of the two previous equations, give an extension of C(s) on the entire plane C except s = 1, as itis illustrated in Fig. 4. The gamma function was alreadv known to Euler. It generalizes the factonal n!. namelv The gamma function was already known to Euler. It generalizes the factorial n!, namely
generally as shown in Figure 6: ReAs’. = Res). 1/2 = Oypyy¢-—1/ 2 = 0.1228 and ReAs,=1/2-—Res, =1/2-—o,,, = 0.1228 iv. If we accept the non-trivial zeroes of the Riemann Zeta Function C(s) as $,= 0) +it, anc
generally as shown in Figure 6: ReAs’. = Res). 1/2 = Oypyy¢-—1/ 2 = 0.1228 and ReAs,=1/2-—Res, =1/2-—o,,, = 0.1228 iv. If we accept the non-trivial zeroes of the Riemann Zeta Function C(s) as $,= 0) +it, anc
b) Solution of the second equation: f=Log[1-z]/Log[z]-2*(2*m)4(-z)*Cos[m*z/2]*Gammal[z];ContourPlot[{Re[f/.z->x+l y]==0,Im[f/.z->x+l y]==0},{x,-15,15},{y,-10,10},ContourStyle->{Red,Blue}] Clear [2]; Schematically we illustrate figure 7 with the program of mathematica: Using the correlation theory and after using Lemma 2 ie.. Log[lim ¢(1—s)/¢(s)]=0 anc Hence the root s and we see a good 20 digit approximation, of upper Re s = 0.5000049 of the order 10°" relations with 1 from 3 groups fields and therefore for our case we will get, if we replace
b) Solution of the second equation: f=Log[1-z]/Log[z]-2*(2*m)4(-z)*Cos[m*z/2]*Gammal[z];ContourPlot[{Re[f/.z->x+l y]==0,Im[f/.z->x+l y]==0},{x,-15,15},{y,-10,10},ContourStyle->{Red,Blue}] Clear [2]; Schematically we illustrate figure 7 with the program of mathematica: Using the correlation theory and after using Lemma 2 ie.. Log[lim ¢(1—s)/¢(s)]=0 anc Hence the root s and we see a good 20 digit approximation, of upper Re s = 0.5000049 of the order 10°" relations with 1 from 3 groups fields and therefore for our case we will get, if we replace
With this analysis, we see that the lower and upper limit converge in the value Res = 1/2, which are the expected results, proving theorem2.
With this analysis, we see that the lower and upper limit converge in the value Res = 1/2, which are the expected results, proving theorem2.
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Discourse AnalysisMathematicsApplied MathematicsNeo-Riemannian AnalysisHistory of MathematicsPhilosophy Of MathematicsPhilosophy of Mathematics EducationNumerical AnalysisComputational MathematicsCompact Riemann surfaces
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